Problem: Simplify to lowest terms. $\dfrac{63}{27}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 63 and 27? $63 = 3\cdot3\cdot7$ $27 = 3\cdot3\cdot3$ $\mbox{GCD}(63, 27) = 3\cdot3 = 9$ $\dfrac{63}{27} = \dfrac{7 \cdot 9}{ 3\cdot 9}$ $\hphantom{\dfrac{63}{27}} = \dfrac{7}{3} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{63}{27}} = \dfrac{7}{3} \cdot 1$ $\hphantom{\dfrac{63}{27}} = \dfrac{7}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{63}{27}= \dfrac{3\cdot21}{3\cdot9}= \dfrac{3\cdot 3\cdot7}{3\cdot 3\cdot3}= \dfrac{7}{3}$